Just in time for a presidential election in which both candidates compete to be besties with Israel, the U.S. and Israeli militaries are holding a big, high-profile exercise to practice shooting Iranian missiles out of the sky. Only neither country wants to say the exercise is about either Iran or presidential politics.

Starting in late October, the U.S. and Israel will spend three weeks jointly testing the abilities of their Patriot missile batteries, Aegis ships, networked command systems and newer interceptors to prevent everything from rockets to armed drones to long-range ballistic missiles from hitting Israel from multiple locations. It’ll be the closest operational look the U.S. has gotten thus far to Israel’s new Iron Dome system to protect against short-range missiles and rockets. About 3,500 U.S. troops will participate in what Lt. Gen. Craig Franklin, commander of the U.S. Third Air Force, called “the largest exercise in the history of the longstanding military relationship between the U.S. and Israel.”

The joint tests, dubbed “Austere Challenge 2012,” are part of a series of missile-defense drills that the U.S. and Israel schedule every two years. Only this year, there’s a contextual difference that’s hard to ignore: the prospect of an Israeli strike on Iran, which is likely to prompt retaliation from Iran and its terrorist proxies on Israel’s borders; and persistent tension between President Obama and Prime Minister Netanyahu, which has become an issue in the politics of both countries. On a conference call with reporters, Franklin and his Israeli colleague, Brig. Gen. Nitzan Nuriel refused to address either issue. The exercise “doesn’t look at any particular threat” and is “not related to national elections,” Franklin insisted.

But that’s hard to believe. The exercise was supposed to happen in the spring, before Israel abruptly requested a rescheduling, prompting a minor media freakout that the U.S. and Israel couldn’t even agree to drill together in the face of the Iranian threat. The rescheduled exercise will feature a smaller number of U.S. troops, which Nuriel characterized as a lighter logistics and support footprint.

Hovering in the background: forthcoming elections in both countries in which bilateral cooperation is an issue. Mitt Romney has made Israel and Iran central to his foreign-policy critique of Obama, contending the president has “thrown Israel under the bus” and vowing to keep any disagreement with Jerusalem over a possible joint Iran strike private. In Israel, former premier Ehud Olmert is considering a challenge to Netanyahu “on a platform accusing Mr. Netanyahu of spoiling Israel’s relations with the United States,” as The New York Times reported Monday. And now Austere Challenge will proceed as Americans go to the polls.

Senior U.S. military officials might have misgivings about attacking Iran, but not to helping Israel repel a missile assault from either Iran or its proxies. The test will be more simulation than live-fire, Franklin and Nuriel said, but will test what Franklin called “new technologies” to stop incoming enemy fire. Those include Israel’s Iron Dome short-range missile and rocket defense system, a piece of hardware that claims an 80 percent success rate against rounds that impact in as little as 12 seconds. The Pentagon helped bankroll it, but doesn’t quite understand how it actually works. And they’ll also practice defending against missiles fired from drones, a drill that has some urgency now that Hezbollah claims responsibility for a drone flown into Israel over the weekend (and which Israel shot down).

Franklin ducked a question about the message Iran should take away from the exercise. Nuriel was blunter. “Everybody can get any type of message he wants from this exercise,” the Israeli general said. “The fact that we are practicing together and working together is a strong message by itself.” And one that might be directed at Americans and Israelis as much as Iranians.